I've been to London several times in February and have found it a superb time to be there. The obvious positives are that it is not so full of tourists and you can often find both good airfares and good hotel rates and you won't encounter huge crowds at museums, etc. I've also had good luck with getting last minute tickets to plays.

Also, don't be so sure that the weather won't be good. As someone from New York State, I find London in February to be absolutely balmy! Seriously, on my February jaunts I've encountered a fair amount of sunshine and very little rain with temperatures ranging from the mid-30s to lower 60s F.

Landra from New York State